CalculateLagrangePolynomials Function

  function CalculateLagrangePolynomials(this,sE) result(lAtS)
    implicit none
    class(Lagrange_t) :: this
    real(prec)      :: sE
    real(prec)      :: lAtS(0:this%N)
    ! Local
    integer    :: j
    logical    :: xMatchesNode
    real(real64) :: temp1,temp2
    real(real64) :: sELocal
    real(real64) :: controlPoints(0:this%N)
    real(real64) :: bWeights(0:this%N)
    real(real64) :: lS(0:this%N)

    sELocal = real(sE,real64)
    do j = 0,this%N
      controlPoints(j) = real(this%controlPoints(j+1),real64)
      bWeights(j) = real(this%bWeights(j+1),real64)
    enddo

    xMatchesNode = .false.

    do j = 0,this%N

      lS(j) = 0.0_real64
      if(AlmostEqual(sELocal,controlPoints(j))) then
        lS(j) = 1.0_real64
        xMatchesNode = .true.
      endif

    enddo

    if(xMatchesNode) then
      do j = 0,this%N
        lAtS(j) = real(lS(j),prec)
      enddo
      return
    endif

    temp1 = 0.0_real64

    do j = 0,this%N
      temp2 = bWeights(j)/(sE-controlPoints(j))
      lS(j) = temp2
      temp1 = temp1+temp2
    enddo

    lS = lS/temp1

    do j = 0,this%N
      lAtS(j) = real(lS(j),prec)
    enddo

  endfunction CalculateLagrangePolynomials